In one of my less developed conlang projects, Janti, I've worked on
including a process of vowel antiharmony. In essence, the language has a
vowel inventory of /a e i o ɵ ɨ/ but adds to this a seventh antiharmonic
morphophoneme //E//. This vowel surfaces usually as an /e/ but if the
previous syllable already has an /e/, it surfaces as an /a/ instead. Hence
you get variation like

tis-nE > tisne
sawa-nE > sawane
koe-nE > koena

I derive this pattern synchronically from a contraction of an earlier
diphthong *aj into *ɛ that then went on to split and merge with either /a/
or /e/. The motivating principle behind this split is pressure for
dissimilation with the previous vowel. The usual outcome was *ɛ > e, but
when the previous vowel was already an original *e, the language rather
went to preserve the lowering vowel height contour and ended up turning
*e(C)ɛ into e(C)a, or *ɛ > a.

The change continued by levelling the resulting /e~a/ alternation in most
cases into either an unalternating /e/ or /a/ but the alternation will
still appear in a few reasonably common inflectional suffixes.

Now, such a dissimilatory process seems pretty natural to me after working
out it's details and I wouldn't be at all surprised to get a case or ANADEW
with it. I just can't think of any language that would have such
antiharmony. Perhaps some of you on the list will know better than me.